Re: [Axiom-developer] Complex exponentiation and 0

[Martin Rubey]

I think Bertfried convinced me. Somehow I did not realize that axiom has
different domains :-) However, I do not yet quite understand how to apply this
insight.

Bertfried Fauser writes:

 > From an algebraic point of view, I think its save to assume 0^0=1 in any
 > category which has _no_ (non-discrete) topological semantics. As eg. real
 > numbers come with a standard topology, 0^0 is not a uniquely definalble
 > object.

Shouldn't this mean that 0^0 is undefined in EXPR INT, for example: x^y ?  Hmm,
I see: in x^y we do not have a problem since there is no zero...

 > Hence as a guidline, every object with allows a "limit" (ie some norm
 > established) should _not_ assume that 0^0=1. I don't see problems for say
 > natural numbers.

So, in other words, there is no bug, except that in

Vanuxem Grégory writes:
> In complex(Float) and Complex(SingleFloat), we have to change the
> exponentiation so that
>         complex(0,0)^complex(0,0.0)
> or
>         complex(0,0)^complex(2,2.0)
> doesn't use log.

the *latter* really should give 0?

--------------------------------------------------------------------

Page, Bill writes:
 > > Maybe as a guide:
 > > 
 > > Mathematica 5.0 for Linux
 > > ...
 > >     |\^/|     Maple 8 (IBM INTEL LINUX)
 > > ...                                       0
 > > 
 > > MuPad also says 0^0=1
 > > ...
 > 
 > I my perhaps less than humble opinion: No!
 > 
 > I think Axiom should *not* use Mathematica, Maple, MuPad or Maxima as a
 > guide. Axiom should only appeal to the mathematics involved. In one way or
 > another all of M^4 (and others) make compromises when it comes to
 > fundamentals. I think Axiom was built with greater respect for the
 > underlying mathematics and that is something that we must retain and
 > nurture. It is the main thing that distinguises Axiom from the others.
 > 
 > Regards,
 > Bill Page.


You are right. However, I still think that we can learn things from M^*. So,
what I should have written is: look, M^* does this and that. Are there things
that are mathematically just and we should incorporate?

Still, I strongly agree with you that we should never be tempted to say: "well,
Mx does it this way, therefore we should do so too."

Martin